Question

A motorboat traveling with a current can go 160km in 4 hours. against the current it takes 5 hours to go the same distance. find the speed of motorboat and speed of current

Answer 1

Speed of the boat=36 km/h

Speed of the current=4 km/h

Explanation:

We have the following data:

`V_(c)=(160 km)/(4 h)=40 km/h` is the speed of the boat traveling with the current

`V_(a)=(160 km)/(5 h)=32 km/h` is the speed of the boat traveling against the current

From here we can write two equations:

`V_(c)=V_(b)+V_(current)` (1)

`V_(a)=V_(b)-V_(current)` (2)

Where
`V_(b)` is the speed of the boat and
`V_(current)` is the speed of the curent

Adding both equations, we have:

`V_(c)+V_(a)=2V_(b)` (3)

Isolating
`V_(b)`:

`V_(b)=(V_(c)+V_(a))/(2)` (4)

`V_(b)=(40 km/h+32 km/h)/(2)` (5)

`V_(b)=36 km/h` (6) This is the speed of the motorboat

Now, substituting (6) in (1):

`40 km/h=36 km/h+V_(current)` (7)

Finding
`V_(current)`:

`V_(current)=4 km/h` (8) This is the speed of the current